The big problem Twisted Transistor had was making people in a remote location easily accessible. We can have the same issue with applications that we write. Often, applications grow, just like Twisted Transistor did - the program might start out as a single-user program, but may expand to allow multiple people to access the program at the same time.
And remember, Java is an object-oriented language, so our real problem is: how do we work it so that programs running one computer can call methods on objects that reside on another? If we can pull this off, then we can distribute the computing load across networks - instead of writing standalone, single user programs, we can write programs that fully utilize our network.
Such programming is often referred to as client/server programming - the program issuing the method calls is the client, and the computer that supplies the remote object is the server.
Twisted Transistor solved their meeting problem by allowing people in separate offices to interact naturally - our goal here is to find technology so that remote and local objects can interact naturally.